Optimal design and hyperbolic problems ∗ †
نویسندگان
چکیده
Quite often practical problems of optimal design have no solution. This situation can be alleviated by relaxation, where one needs generalised materials which can mathematically be defined by using the theory of homogenisation. First mathematical results in this direction for general (nonperiodic) materials were obtained by Murat and Tartar. We present some results in optimal design where the equation of state is hyperbolic. The control function is related to the response of vibrating material under the given external force. As the problem under consideration has no solution, we consider its relaxation to H-closure of the original set of controls.
منابع مشابه
Multigrid Methods for PDE Optimization
Research on multigrid methods for optimization problems is reviewed. Optimization problems include shape design, parameter optimization, and optimal control problems governed by partial differential equations of elliptic, parabolic, and hyperbolic type.
متن کاملSOLVING LINEAR SIXTH-ORDER BOUNDARY VALUE PROBLEMS BY USING HYPERBOLIC UNIFORM SPLINE METHOD
In this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6VBP ) by using the hyperbolic uniform spline of order 3 (lower order). Thereis proved to be first-order convergent. Numerical results confirm the order of convergencepredicted by the analysis.
متن کاملThe Optimal Allocation of Iran's Natural Gas
T he optimal allocation of natural gas resources to various uses such as final and intermediate consumption, injection into oil fields, and exports can help policymakers to use this kind of resources efficiently. Empirical evidence support using hyperbolic discount rates instead of fixed discount rates in the economic literature. The purpose of this study is to maximize the social we...
متن کاملExistence of Solutions and Optimal Control Problems for Hyperbolic Hemivariational Inequalities
In this paper we prove the existence of solutions for hyperbolic hemivariational inequalities and then investigate optimal control problems for some convex cost functionals.
متن کاملOptimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006